Bounds on the Crosscap Number of Torus Knots

Details Bounds on the Crosscap Number of Torus Knots Bounds on the Crosscap Number of Torus Knots

2004-09-29

arxiv.org/abs/math/0409581v2

Mathematics

Geometric Topology

7 Pages, 0 figures Version 2 - corrected a typo: Clark showed c(K) \le 2g(K) + 1

Scientific paper

For a torus knot K, we bound the crosscap number c(K) in terms of the genus
g(K) and crossing number n(K): c(K) \leq [(g(K)+9)/6] and c(K) \leq [(n(K) +
16)/12]. The (6n-2,3) torus knots show that these bounds are sharp.

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